I have been working on visualizing 4-dimensional things for a while now. I have not been especially successful (I can sort of see a tesseract end-on, but not much else), but it got me to thinking about how vision works. When we learn to see, our brain uses tons of sample data (both visual & kinesthetic) to fine tune its model of the world. Unfortunately, I am both past the stage of development where such things are usually learned & not aware of any actual 4-dimensional experiences to be had.
Feel free to try the things I describe (at your own risk), but if you get it to work, I would appreciate it if you would release it for free as I have done (software, anyway - for hardware I ask only that you do not patent it). I will update this page if I get any of it to work. I also ask that you try to use the terms in the Tetraspace glossary for consistency, in things like user interfaces. Granted, some of the terms are a bit of a stretch (especially the directional terms, which I hope are replaced once someone gets an intuitive feel for 4D), but things like tesseract, glome, & realm seem pretty reasonable. Of course if you find a new kind of object or situation you can name it whatever you want.
One obvious thing (just barely feasible with existing technology) would be to feed 4-D images (well, 3-D image data depicting 4-D scenes) into a person's brain in a similar manner to that used to give sight to those with defective eyes. This would work, & if done early enough, the brain should learn to arrange it into a mental picture. There are several other issues, such as simulating saccades (which now must have 3 independent directions of movement) & user interaction (since, as mentioned before, kinesthetic interaction helps us get a feel for the 3-D-ness of the world). However, I doubt I could convince someone to fund research on little kids in what amounts to unproven methods of brain augmentation with no immediate purpose, & they are even less likely to fund me testing it on myself (given the widespread belief that fully-developed brains cannot learn such fundamentally new things).
So I propose to route the information through pathways accessible externally via consumer hardware. Image data can be projected onto the retinas using something like a head-mounted display. A volume of points must be mapped into an area of points, preferably preserving radii, due to the layout of the receptors in the retina. (I tried using a space-filling curve mapping, but my mind refused to see anything other than a jumble of points. YMMV.) If the image is moved to be kept fixed with respect to the retina & eye movements are used to update the virtual camera's position, it will make it easier for the brain to learn the mapping. An EEG signal (or a combination of EEG signals) could be used to provide the additional degree of freedom of eye movement.
Obviously rendering will be an issue since there are (to my knowledge) not yet any 4-D hardware accelerators, but the problem is not as hopeless as it seems at first. If we keep the image fixed on the retina, we can reduce the detail of the outer edges with no perceptible loss of quality, & there will not be more voxels than there are pixels in the 3-D case - they will merely be arranged differently. So software rendering should suffice for simple scenes. On the other hand, the images ought to be as realistic as possible, since they will be the basis on which people form their intuition about 4-D things. While there are no 4-dimensional things on which to base the renderer, I think the most reasonable thing to use would be something like path tracing, which automatically accounts for the dimensionality of space. This should produce results closest to what a "real" 4-dimensional universe would (as long as nobody tries to do quantum physics experiments).
It is probably best to do the training in the form of an interactive first-person game. I suggest having moving shapes (say, the 6 platonic solids) & having the user try to aim at a specific shape. Controlling movement & aiming at the same time might be a bit tricky, since there are then 8 degrees of freedom. This can be reduced to 6 if you keep the user on a ground realm (3-hyperplane) & keep their head upright. A 3-D mouse plus 6 directional keys & a key to jump might suffice (based on existing 3-D first-person games).
While head tracking helps with realism, it might be a bit difficult to find the extra 2 degrees of freedom (one rotational & one translational). These would have to be from EEG data, since the user's hands are already busy moving their virtual body, & using appendages for head movement would defeat the purpose of head tracking anyway. On the other hand, if you can extract 3 continuous degrees of freedom from EEG data reliably, that would give the best overall experience.
If a 4-D computer interface is not readily available (& the ones described above are not exactly cheap), then I will have to make do with what I have in my head, plus whatever I can get out of ordinary 2-D diagrams & such. I have tried to imagine stacking numerous 3-D slices together, but I have trouble keeping them ordered in my mind. Another possibility is to imagine the space around you filled with 3-D shadows that 4-D objects would cast as a light moves around. This works, but it does not really tell you much about how the object itself looks. (Remember Plato's Allegory of the Cave?) The next logical step would be to imagine the 3-D images formed by 4-D scenes. I suppose that if you did it long enough you might get your brain to fill in the original 4-D scene (like how after a while of seeing 2-D images the brain starts filling in the 3-D world), but I just started, so I have nothing to report yet. One thing of particular importance is to make sure you have the correct distance information assigned, not the 3-D distances apparent in the image itself, or else your brain will just interpret it as a 3-D scene.
I regularly have lucid dreams. I would like to try dreaming in 4D, but I can only control my dreams after they start, & I usually forget what I intended to do. I might also try brainwave entrainment to get into the right state of mind without forgetting my goal, but school is currently in the way of anything that takes too much time. If it works, dreaming in 4D would be the best solution of all, since it would be completely immersive. Realism might suffer as it does in all dreams, but there is no reason to suppose that your brain would not, for example, make light behave more or less like it does in 3D (which is a pretty good approximation, falloff differences aside). If you want to try this path, be sure to read a lot about what 4-D objects are like (say, at Tetraspace) so that you have something off which to base your dreams.
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